Express as a single logarithm.
log(subsript)5�ã175-log(subscript)5�ã7
x =log5 (sqrt 175) - log5 (sqrt 7)
x = log 5 (sqrt 175/7)
x= log 5(25)
5^x = 25
x = 2
I did those last couple of steps in my head, here is the way to do it methodically:
x= log5(25)
x = log5 (5^2)
x = 2 log5(5) but log5(5) = 1
x = 2
To express the given expression as a single logarithm, you can use the logarithmic property that states log(base a) b - log(base a) c = log(base a) (b/c). Here's how you can apply this property in this case:
Given: log(subscript)5�ã175 - log(subscript)5�ã7
By using the property, we can combine the two logarithms into a single logarithm:
log(subscript)5 (�ã175/�ã7)
Now, simplify the expression inside the logarithm:
log(subscript)5 (�ã25)
Since the square root of 25 is 5, we have:
log(subscript)5 (5)
Finally, note that log(base a) a = 1. Therefore:
log(subscript)5 (5) = 1
Hence, the expression log(subscript)5�ã175 - log(subscript)5�ã7 can be expressed as a single logarithm, which is simply 1.